DOI QR코드

DOI QR Code

Sampled-data Fuzzy Observer Design for an Attitude and Heading Reference System and Its Experimental Validation

  • Kim, Han Sol (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Park, Jin Bae (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Joo, Young Hoon (Dept. of Control and Robotics Engineering, Kunsan National Universitty)
  • 투고 : 2017.05.15
  • 심사 : 2017.08.05
  • 발행 : 2017.11.01

초록

In this paper, a linear matrix inequality-based sampled-data fuzzy observer design method is proposed based on the exact discretization approach. In the proposed design technique, a numerically relaxed observer design condition is obtained by using the discrete-time fuzzy Lyapunov function. Unlike the existing studies, the designed observer is robust to the uncertain premise variable because the fuzzy observer is designed under the imperfect premise matching condition, in which the membership functions of the system and observer are mismatched. In addition, we apply the proposed method to the state estimation problem of the attitude and heading reference system (AHRS). To do this, we derive a Takagi-Sugeno fuzzy model for the AHRS system, and validate the proposed method through the hardware experiment.

키워드

참고문헌

  1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, 1985. https://doi.org/10.1109/TSMC.1985.6313399
  2. J. Yoneyama, "$H_{\infty}$ filtering for fuzzy systems with immeasurable premise variables: an uncertain system approach," Fuzzy Sets Syst., vol. 160, pp. 1738-1748, 2009. https://doi.org/10.1016/j.fss.2008.09.012
  3. H. J. Kim, J. B. Park, and Y. H. Joo, "Decentralized H_${\infty}$ fuzzy filter for non-linear large-scale systems under imperfect premise matching," IET Cont. Theo. Appl., vol. 18, no. 9, pp. 2704-2714, 2015.
  4. J. Zhang, P. Shi, J. Qiu, and S. K. Nguang, "A novel observer-based output feedback controller design for discrete-time fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 23, no. 1, pp. 223-229, 2015. https://doi.org/10.1109/TFUZZ.2014.2306953
  5. X. Xie, D. Yang, and H. Ma, "Observer design of discrete-time T-S fuzzy systems via multi-instant homogenous matrix polynomials," IEEE Trans. Fuzzy Syst., vol. 22, no. 6, pp. 1714-1719, 2014. https://doi.org/10.1109/TFUZZ.2014.2302491
  6. T. Chen and B. A. Francis, "Optimal sampled-data control systems," Springer, 2012.
  7. D. W. Kim, H. J. Lee, and M. Tomizuka, "Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach," IEEE Trans. Fuzzy Systs., vol. 18, no. 2, pp. 251-260, 2010.
  8. D. W. Kim and H. J. Lee, "Sampled-data observerbased output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach," Fuzzy Sets and Syst., vol. 201, pp. 20-39, 2012. https://doi.org/10.1016/j.fss.2011.12.017
  9. D. W. Kim, J. B. Park, and Y. H. Joo, "Effective digital implementation of fuzzy control systems based on approximate discrete-time models," Automatica, vol. 43, pp. 1671-1683, 2007. https://doi.org/10.1016/j.automatica.2007.01.025
  10. G. B. Koo, J. B. Park, and Y. H. Joo, "Decentralized sampled-data fuzzy observer design for nonlinear interconnected systems," IEEE Trans. Fuzzy Syst., vol. 24, no. 3, pp. 661-674, 2016. https://doi.org/10.1109/TFUZZ.2015.2470564
  11. K. Tanaka and H. O. Wang, "Fuzzy control systems design and analysis: a linear matrix inequality approach," Wiley, 2001.
  12. T. M. Guerra and V. Laurent, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugen's form," Automatica, vol. 40, pp. 823-829, 2004. https://doi.org/10.1016/j.automatica.2003.12.014
  13. X. Xie, D. Yue, and X. Zhu, "Further studies on control synthesis of discrete-time T-S fuzzy systems via useful matrix equalities," IEEE Trans. Fuzzy Syst., vol. 22, no. 4, pp. 1026-1031, 2014. https://doi.org/10.1109/TFUZZ.2013.2277583
  14. X. P. Xie and S. L. Hu, "Relaxed stability criteria for discrete-time Takagi-Sugeno fuzzy systems via new augmented nonquadratic Lyapunov functions," Neurocom., vol. 166, pp. 416-421, 2015. https://doi.org/10.1016/j.neucom.2015.03.038
  15. S. Bouabdallah, A. Noth, and R. Siegwart, "PID vs LQ control techniques applied to an imdoor micro quadrotor," IEEE/RSJ Int. Conf. on Intel., Robots, Syst., pp. 2451-2456, 2004.
  16. S. O. H. Madgwick, A. J. L. Harrison, and R. Vaidyanathan, "Estimation of IMU and MARG orientation using a gradient decent algorithm," IEEE Conf. Rehab. Robot., pp. 1-7, 2011.
  17. R. E. Kalman, "A new approach to linear filtering and prediction problems," J. Basic Eng., vol. 82, pp. 35-45, 1960. https://doi.org/10.1115/1.3662552
  18. W. Li and J. Wang, "Effective adaptive Kalman filter for MEMS-IMU/Magnetometers integrated attitude and heading reference systems," J. Nav., vol. 66, pp. 99-113, 2013. https://doi.org/10.1017/S0373463312000331
  19. M. Wang, Y. Yang, R. R. Hatch, and Y. Zhang, "Adaptive filter for a miniature MEMS based attitude and heading reference system," Pos. Local. Nav. Sympo., pp. 26-29, 2004.
  20. T. S. Yoo, S. K. Hong, H. M. Yoon, and S. Park, "Gain-scheduled complementary filter design for a MEMS based attitude and heading reference system," Sensors, vol. 11, pp. 3816-3830, 2011. https://doi.org/10.3390/s110403816
  21. R. B. Widodo, H. Edayoshi, and C. Wada, "Complementary filter for orientation estimation: adaptive gain based on dynamic acceleration and its change," SCIS and ISIS 2014, pp. 906-909, 2014.
  22. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. 39th IEEE Conf. Decis. Cont., pp. 2805-2810, 2000.
  23. G. B. Koo, J. B. Park, and Y. H. Joo, "Guaranteed cost sampled-data fuzzy control for non-linear systems: A continuous-time Lyapunov approach," IET Cont. Theo. Appl., vol. 7, no. 13, pp. 1745-1752, 2013. https://doi.org/10.1049/iet-cta.2013.0186
  24. J. Lofberg, "YALMIP: a toolbox for modeling and optimization in MATLAB," in Proc. CACSD Conf., pp. 284-289, 2004.
  25. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Opt. Meth. Soft., vol. 11, pp. 625-653, 1999. https://doi.org/10.1080/10556789908805766